On a sequence formed by iterating a divisor operator

Djamel, Bellaouar, Abdelmadjid, Boudaoud, and Özer, Özen. "On a sequence formed by iterating a divisor operator." Czechoslovak Mathematical Journal 69.4 (2019): 1177-1196. <http://eudml.org/doc/294676>.

@article{Djamel2019,
abstract = {Let $\mathbb \{N\}$ be the set of positive integers and let $s\in \mathbb \{N\}$. We denote by $d^\{s\}$ the arithmetic function given by $ d^\{s\}( n) =( d( n) ) ^\{s\}$, where $d(n)$ is the number of positive divisors of $n$. Moreover, for every $\ell ,m\in \mathbb \{N\}$ we denote by $\delta ^\{s,\ell ,m\}( n) $ the sequence \[ \underbrace\{d^\{s\}( d^\{s\}( \ldots d^\{s\}( d^\{s\}( n) +\ell ) +\ell \ldots ) +\ell ) \}\_\{m\text\{-times\}\} =\{\left\lbrace \begin\{array\}\{ll\} d^\{s\}( n) & \text\{for\} \ m=1,\\ d^\{s\}( d^\{s\}( n) +\ell ) &\text\{for\} \ m=2,\\ d^\{s\}(d^\{s\}( d^\{s\}(n) +\ell ) +\ell ) & \text\{for\} \ m=3, \\ \vdots & \end\{array\}\right.\} \] We present classical and nonclassical notes on the sequence $ ( \delta ^\{s,\ell ,m\}( n)) _\{m\ge 1\}$, where $\ell $, $n$, $s$ are understood as parameters.},
author = {Djamel, Bellaouar, Abdelmadjid, Boudaoud, Özer, Özen},
journal = {Czechoslovak Mathematical Journal},
keywords = {divisor function; prime number; iterated sequence; internal set theory},
language = {eng},
number = {4},
pages = {1177-1196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a sequence formed by iterating a divisor operator},
url = {http://eudml.org/doc/294676},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Djamel, Bellaouar
AU - Abdelmadjid, Boudaoud
AU - Özer, Özen
TI - On a sequence formed by iterating a divisor operator
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1177
EP - 1196
AB - Let $\mathbb {N}$ be the set of positive integers and let $s\in \mathbb {N}$. We denote by $d^{s}$ the arithmetic function given by $ d^{s}( n) =( d( n) ) ^{s}$, where $d(n)$ is the number of positive divisors of $n$. Moreover, for every $\ell ,m\in \mathbb {N}$ we denote by $\delta ^{s,\ell ,m}( n) $ the sequence \[ \underbrace{d^{s}( d^{s}( \ldots d^{s}( d^{s}( n) +\ell ) +\ell \ldots ) +\ell ) }_{m\text{-times}} ={\left\lbrace \begin{array}{ll} d^{s}( n) & \text{for} \ m=1,\\ d^{s}( d^{s}( n) +\ell ) &\text{for} \ m=2,\\ d^{s}(d^{s}( d^{s}(n) +\ell ) +\ell ) & \text{for} \ m=3, \\ \vdots & \end{array}\right.} \] We present classical and nonclassical notes on the sequence $ ( \delta ^{s,\ell ,m}( n)) _{m\ge 1}$, where $\ell $, $n$, $s$ are understood as parameters.
LA - eng
KW - divisor function; prime number; iterated sequence; internal set theory
UR - http://eudml.org/doc/294676
ER -